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In this talk, we present the QCD factorization formula for heavy quarkoniumproduction at large $p_T$ with factorized leading-power and next-to-leadingpower contributions in the $1/p_T$ expansion. We show that the leading orderanalytical calculations in this QCD factorization approach can reproduceeffectively the full next-to-leading order numerical results derived usingnon-relativistic QCD (NRQCD) factorization formalism. We demonstrate that thenext-to-leading power contributions are crucial to the description of thechannels that are the most relevant for the rate as well as polarization of$J/\psi$ production at current collider energies.

QCD factorization for high $p_T$ heavy quarkonium production